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## Difference between square root/square

This topic has 2 expert replies and 3 member replies
ildude02 Master | Next Rank: 500 Posts
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#### Difference between square root/square

Mon Jun 23, 2008 7:25 pm
I wanted to understand the difference between X^2 =Y vs x = SQRT(Y),

eg: say x^2 = 36, x can be a +ve 6 or a -ve 6. But if X = SQRT(36), then x = 6 since I beleive that given a SQRT of a number, we can only take positive values. Am I right in making that statement.

In that regard, my question is, if I see a DS question asking for value of x, and if the statements are;

1) x^2 = 36;
2)x = SQRT(36)

Can I safely say, B is SUFFICIENT?

In the same regard, an other flavour of the question is,

Is the value of x + y = 0?

1) xy < 0
2)x^2 = y^2

Last edited by ildude02 on Mon Jun 23, 2008 8:38 pm; edited 1 time in total

### GMAT/MBA Expert

Ian Stewart GMAT Instructor
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Mon Jun 23, 2008 7:50 pm
ildude02 wrote:
eg: say x^2 = 36, x can be a +ve 6 or a -ve 6. But if X = SQRT(36), then x = 6 since I beleive that given a SQRT of a number, we can only take positive values. Am I right in making that statement.
Technically, in math-speak, we say that the square root symbol gives the "non-negative square root", (and not the 'positive root') because the result might be equal to zero (which only happens if you take the SQRT of zero). If you see the square root symbol -- which you see in many GMAT questions -- that symbol means 'the non-negative square root'; SQRT(36) is equal to 6. But, as you point out, if x^2 = 36, all you can say is that x = 6 or x = -6; there's no way to find an exact value for x.

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ildude02 Master | Next Rank: 500 Posts
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Mon Jun 23, 2008 8:42 pm
Ian, can we assume that when an equation looks like, x = SQRT(y^2), it doesn't mean that x= y, but it can be either be y or -y as in |y| ?

durgesh79 Master | Next Rank: 500 Posts
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Mon Jun 23, 2008 9:08 pm
x = SQRT(y^2) means x = y. it doest mean x= -y

however if x^2 = y^2, then x = +/- y.

statement 1 : xy < 0 tells that x and y have opp signs. Not suff

statement 2 : x^2 = y^2

(x+y)(x-y) = 0
so either x = - y
or x = y
Not suff

combine both 1 and 2. x = -y so x+y = 0. Suff .. answer C

### GMAT/MBA Expert

Ian Stewart GMAT Instructor
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Tue Jun 24, 2008 3:43 am
durgesh79 wrote:
x = SQRT(y^2) means x = y. it doest mean x= -y
No, ildude was correct here. If you have the equation x = SQRT(y^2), then x cannot be negative, but y can be negative. So x = |y|. Try this with numbers- let y = -6. Then x will not be equal to y.

durgesh79 Master | Next Rank: 500 Posts
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Wed Jun 25, 2008 10:53 pm
Ian Stewart wrote:
durgesh79 wrote:
x = SQRT(y^2) means x = y. it doest mean x= -y
No, ildude was correct here. If you have the equation x = SQRT(y^2), then x cannot be negative, but y can be negative. So x = |y|. Try this with numbers- let y = -6. Then x will not be equal to y.
yes i agree, Thanks for correcting

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